Isospectral Manifold Learning Algorithm And Its Application

Spectral learning is a new method in the field of machine learning, which has causeduniversal attention. In this paper, we mainly study the questions of isopectral manifold andpropose the frame of isopectral manifold learning which includes:1) Giving the relationship between the spectral method and manifold learning andgiving solid theoretical proofs, which laid the theoretical foundation for this paper;2) Giving isopectral manifold learning algorithm which gets the reasonableneighborhood size and neighboring weights from the full view. IMLA takes into accountthe discriminant supervision information. Thus, it not only preserves the sparsereconstructive relationship, but also sufficiently utilizes discriminant information;3) Giving fast learning algorithm of spectral manifold which reduces thecomputational complexity of calculating spectral values. FSM reduces the computationalcomplexity of calculating spectral values from the construction of the anchor figure andlinearized manifold learning approach;4) Giving multi-manifold isopectral learning algorithm which finds the solution thatthe traditional manifold learning algorithms can’t handle the multi-data well.MMILAassumes that multi-type data are the uniform distribution on different multiple manifold.Putting isospectral manifold learning algorithm on multi-manifold in order to find thesolution of handling multi-type data;5) Putting the algorithms to face recognition and verifying the effectiveness of themethod by experiments.In summary, on the basis of the question of isopectral manifold, we propose a newisopectral manifold learning methods.Although we have achieved some success, there are a lot of work about spectral learning, such as isopectral mapping learning problems、isopectral embedding learning problems、isopectral topological computing problems, andso on.